Scattering matrices for dissipative quantum systems
Abstract
We consider a quantum system S interacting with another system S and susceptible of being absorbed by S. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H0 + V -- iC * C. The generator of the free dynamics, H0, is self-adjoint, V is symmetric and C is bounded. We study the scattering theory for the pair of operators (H, H0). We establish a representation formula for the scattering matrices and identify a necessary and sufficient condition to their invertibility. This condition rests on a suitable notion of spectral singularity. Our main application is the nuclear optical model, where H is a dissipative Schr{\"o}dinger operator and spectral singularities correspond to real resonances.
Keywords
Cite
@article{arxiv.1808.09179,
title = {Scattering matrices for dissipative quantum systems},
author = {Jérémy Faupin and Francois Nicoleau},
journal= {arXiv preprint arXiv:1808.09179},
year = {2018}
}